The largest difference between the multi-scale model and previous work [58,59], is the ability to take into account, even in an approximate way, the redistribution of cement due to the presence of the aggregates. This gives more accurate values of DITZ and D bulk. This step appears to be crucial, especially at the high volume fractions of aggregate common in concrete, as this redistribution of cement plays an important role in determining the bulk properties of the concrete. The procedure used in the multi-scale model to determine this ratio, step (2) as given above, is still approximate, since the gradient of properties in the interfacial zone is treated as being equivalent to a fixed width, fixed property interfacial zone surrounded by fixed property bulk cement paste.
One consequence of this cement redistribution is a sort of "negative feedback" loop, in the following sense. Suppose the interfacial transition zone is made wider, by using a coarser cement, perhaps. This would tend to drive up the value of D ITZ, and lower the value of D bulk, so that the ratio of the two would be larger, implying a larger value of D/Dbulk [58]. However, the actual value of D will not be as much higher as one might predict, since the higher value of D/Dbulk must be multiplied by the lower value of Dbulk to get the overall concrete diffusivity. So just increasing the diffusivity of the interfacial zone by thickening it will not increase the overall concrete diffusivity as much as might be expected [6]. Increasing the surface area of the aggregate by reducing the average aggregate diameter results in similar behavior. Other interplays between the variables of the problem are discussed in Ref. [6], which used a statistically designed model experiment to probe which microstructural variables were significant. These were found to be: aggregate volume fraction, w/c ratio, and degree of hydration, with the thickness of the interfacial transition zone still significant but to a lesser extent.
In order to properly compare the model with experimental results, one cannot just prepare concretes at various aggregate volume fractions, and then simply normalize the concrete measurements by cement paste measurements taken at equal times. The redistribution of cement in the concrete makes the value of Dbulk in the concrete not the same as the plain cement paste sample, even at equal degrees of hydration. What must be done experimentally is the following. The degree of hydration of the concrete must be determined, along with the volume fraction and particle size distribution of the aggregates, and the particle size distribution of the cement, or at least its median particle size. These are the necessary microstructural variables on which the multi-scale model operates. The diffusivity or electrical conductivity of the concrete can then be measured and compared with model predictions. This procedure has been been carried out for mortars with various amounts of sand [60].